High Precision Numerical Study For High Frequency Dynamic Problem Of Saturated Geotechnical Medium In Time Domain

In practical engineering,such as excavation of tunnel and slope,underwater blasting,compaction of weak foundation,etc.,the high frequency dynamic response of saturated geotechnical medium is involved in a large number of problems.This problem has become a hot research issue in the field of science and engineering.In this paper,two numerical solutions for analyzing the high frequency dynamic problems of saturated geotechnical medium are proposed based on the u-w format and the u-U format dynamic governing equations.The two numerical solutions adopt standard finite element method to discretize space in space domain and introduce precise time step integration method in time domain.Through spectral radius analysis of the transfer matrix and error analysis,it is proved that the two schemes are unconditionally stable and the numerical error do not accumulate with the calculation.This paper mainly completes the following contents:(1)The proposed scheme is firstly used to solve the one-dimensional dynamic problem of saturated geotechnical medium,and the accuracy of the DPTSIM:u-w numerical scheme and DPTSIM:u-U numerical scheme are preliminarily verified by comparison with the analytical solution.And the effect of permeability on one-dimensional dynamic response is analyzed.(2)The dynamic response problem of saturated geotechnical medium in two-dimensional finite domain and semi-infinite space domain is analyzed by using the proposed numerical scheme.The numerical solution is compared with the calculation results of Newmark:u-w scheme and Newmark:u-U scheme.The comparison results show that the proposed scheme can still obtain accurate numerical results under large time step.At the same time,we calculated the dynamic response of two saturated geotechnical medium models at different load frequencies,and compared the solution results with those of DPTSIM numerical scheme to analyze the accuracy of our proposed scheme in solving high-frequency dynamic problems.(3)The dynamic response of infinite cylindrical cavity in saturated geotechnical medium under impact load is solved,which is compared with the results of previous studies to verify the high accuracy of the numerical solution in time domain.The influence of load frequency,ratio and porosity on dynamic response of cavity model is analyzed.